Flood Risk Mapping with Synthetic Rating Curves and DEMs: A Practical GIS Tutorial

Introduction

Flood risk mapping combines terrain analysis, river hydraulics, and hydrological frequency estimates to identify areas that may become inundated during high-flow events. A Digital Elevation Model (DEM) provides the terrain surface, while a river stage–discharge relationship, commonly called a rating curve, links river discharge to water-surface elevation.

Flood Risk Mapping Synthetic Rating Curves DEM workflows are useful for preliminary flood screening, catchment planning, infrastructure assessment, and identifying communities potentially exposed to river flooding. When measured river-stage data or detailed hydraulic models are unavailable, a synthetic rating curve can provide an initial estimate of flood levels using channel geometry, channel slope, and an assumed hydraulic roughness coefficient.

However, a synthetic rating curve does not directly predict flood extent. It estimates water levels for specified discharges under simplified hydraulic assumptions. GIS terrain processing then uses those levels to estimate inundation extent and depth.

This tutorial develops a practical workflow using QGIS, a DEM, river cross-sections, Manning’s equation, and raster calculations to produce indicative flood maps for the 10-year, 50-year, and 100-year return periods.

The workflow follows five main stages:

1. Extract channel and floodplain cross-sections from the DEM.

2. Calculate synthetic stage–discharge relationships using Manning’s equation.

3. Estimate design flood discharges and corresponding water levels.

4. Interpolate or assign water-surface elevations across the floodplain.

5. Subtract terrain elevation from water-surface elevation to derive flood depth and inundation extent.

The important distinction is that this is a simplified GIS-based hydraulic screening method, not a replacement for a calibrated one-dimensional or two-dimensional hydrodynamic model.

1. Core concepts and governing equations

1.1 Digital Elevation Models and channel geometry

A DEM represents terrain elevation as a regular grid of cells. Each cell stores an elevation, typically in metres above a vertical datum.

For river flood modeling, the DEM should represent both the river channel and the surrounding floodplain. Its resolution and vertical accuracy directly affect the reliability of extracted cross-sections and calculated inundation depths.

Useful inputs include:

• A bare-earth DEM, preferably with reliable channel bathymetry.

• A river centerline or stream network.

• Catchment boundaries and drainage characteristics.

• River slope estimated from surveyed elevations or the DEM.

• Channel roughness estimates based on bed material, vegetation, and channel condition.

• Design discharges for the 10-year, 50-year, and 100-year return periods.

Important: Many surface DEMs derived from satellite imagery do not accurately represent submerged riverbeds. Bridges, embankments, vegetation, and buildings can also introduce artificial barriers or elevations. A DEM that omits the channel bed may substantially misrepresent channel capacity.

1.2 River cross-sections

A river cross-section is a profile of elevation against horizontal distance across the channel and adjoining floodplain.

Cross-sections provide the geometry needed to estimate the flow area, wetted perimeter, and hydraulic radius at different water levels.

For a channel section:

where:

• \(A\) is the area of the portion of the cross-section below the water surface, in \(\mathrm{m^2}\).

• \(P\) is the length of the channel boundary in contact with water, in metres.

• \(R\) is the hydraulic radius, in metres.

The hydraulic radius is not the same as the channel’s geometric radius. It describes how much flow area is available relative to the wetted boundary.

For example, a deeper, relatively narrow channel may have a larger hydraulic radius than a shallow, broad channel, depending on its geometry.

1.3 Manning’s roughness coefficient

Manning’s roughness coefficient, \(n\), represents resistance to flow from the channel bed, banks, vegetation, and other surface characteristics.

Typical preliminary ranges vary considerably with site conditions:

These are indicative ranges, not universal design values. The appropriate coefficient should be selected using field observations, published hydraulic references, or calibration against measured water levels and discharge.

A single roughness coefficient for the entire floodplain is rarely appropriate. Vegetated floodplains, cultivated land, built-up areas, and the main channel can have very different flow resistance.

1.4 Manning’s equation for discharge

For steady, approximately uniform open-channel flow in SI units, Manning’s equation is:

where:

• \(Q\) = discharge, in \(\mathrm{m^3/s}\).

• \(n\) = Manning’s roughness coefficient.

• \(A\) = wetted cross-sectional area, in \(\mathrm{m^2}\).

• \(R\) = hydraulic radius, in metres.

• \(S\) = energy slope, dimensionless.

For preliminary calculations, the energy slope is sometimes approximated by the channel-bed slope. This assumption is most defensible under approximately uniform flow; it may be unsuitable near backwater effects, confluences, bridges, abrupt channel changes, or rapidly varying flow.

The equation can also be rearranged to estimate a required hydraulic conveyance for a specified discharge:

where

Here, \(K\) is the section’s hydraulic conveyance under the specified geometry and roughness assumptions.

By calculating \(A\), \(P\), and \(R\) for multiple trial water levels, it is possible to construct a synthetic rating curve linking stage to discharge.

2. Step-by-step execution workflow in QGIS

Step 1: Prepare the DEM and river network

Begin by loading the DEM, river centerline, and catchment boundary into QGIS.

Recommended preparatory processing:

• Fill or correct DEM artifacts only where appropriate. Do not indiscriminately fill depressions that represent real floodplain features.

• Generate a hillshade to inspect channel alignment and floodplain morphology.

• Extract the longitudinal river profile and estimate channel slope between representative locations.

• Check for bridges, culverts, levees, and embankments that may control flood conveyance.

Raster alignment matters. Later raster calculations should use compatible coordinate systems, cell sizes, extents, and grid alignment. Otherwise, subtraction can introduce interpolation errors or shift the resulting flood-depth map.

Step 2: Extract river cross-sections from the DEM

Cross-sections should generally be oriented perpendicular to the local river flow direction. They should extend beyond the expected floodplain boundary on both sides of the river.

A practical starting point is to place cross-sections at regular intervals along the river, then add sections at bends, tributaries, bridges, constrictions, and substantial changes in valley geometry. The appropriate spacing depends on the complexity of the reach and the DEM resolution.

2.1 Generate transects

In QGIS, use the Processing Toolbox to create points along the river centerline and generate perpendicular transects with a suitable line-processing algorithm or a cross-section plugin.

For each transect, record:

• Cross-section identifier.

• River station or chainage.

• Horizontal distance along the transect.

• DEM elevation at each sampled position.

• Main-channel width and bank elevations.

• Floodplain elevations and potential obstructions.

Transects must span the full potential inundation corridor. A section that ends within the floodplain may underestimate the area available to convey flow.

2.2 Sample elevations

Use Processing Toolbox → Sample raster values to attach DEM elevations to points along the transects. Alternatively, use GDAL-based profile tools or Python with Rasterio to extract the elevation profile.

For each cross-section, construct an elevation-distance series:

Illustrative data only; these are not field measurements.

This profile indicates a relatively low section near the channel center, with higher ground toward the banks. In a real cross-section, use sufficiently dense sampling to preserve channel shape and floodplain features.

2.3 Calculate wetted geometry at trial stages

Suppose the trial water-surface elevation is \(z_w\), and the ground elevation at sample point \(i\) is \(z_i\).

The local water depth is:

For adjacent sample points separated by horizontal distance \(\Delta x\), estimate the wetted area using trapezoidal integration:

This assumes a common horizontal spacing; for variable spacing, use the individual distance between samples.

The wetted perimeter can be approximated by summing the lengths of the submerged portions of the channel boundary. Where an adjacent segment crosses the waterline, interpolate the intersection rather than counting the entire segment.

Then calculate:

Repeat these calculations for multiple trial stages above the channel bed and bank elevations.

Hydraulic caution: If a cross-section contains a main channel and separate floodplain flow paths, calculating one combined wetted perimeter and applying one roughness coefficient can produce poor results. More realistic calculations divide the section into subsections with separate roughness values and account for conveyance between them.

Step 3: Build synthetic stage–discharge rating curves

Once the geometry has been calculated for a series of trial stages, apply Manning’s equation to each stage.

For trial stage \(j\):

A rating curve plots water-surface elevation or stage on the vertical axis against calculated discharge on the horizontal axis. If stage is measured relative to a gauge datum, retain that datum consistently.

3.1 Construct the curve

Calculate discharge at a range of stages, for example at 0.1–0.25 m elevation increments, adjusting the increments to the channel geometry and DEM accuracy.

The table is a calculation template: actual values must come from the sampled cross-section.

Plot the calculated stage–discharge pairs in a spreadsheet or Python. A monotonic curve is usually expected under the assumed steady-flow conditions. Investigate non-monotonic results for geometry errors, changing flow paths, or inappropriate roughness assignments.

If a design discharge falls between two calculated points, interpolate within the valid range. Avoid extrapolating well beyond the calculated stage range without additional hydraulic analysis.

Step 4: Estimate the 10-year, 50-year, and 100-year flood discharges

A return period describes the annual exceedance probability of a flow magnitude under a stationary probability model.

For a return period \(T\):

Therefore:

A 100-year flood is not guaranteed to occur only once every 100 years. Events of this magnitude can occur in consecutive years.

Design discharges should be estimated from suitable observed annual-maximum flow data, a regional flood-frequency analysis, or an appropriate hydrological model. They cannot be derived from the DEM alone.

For illustration, suppose an independent hydrological study provides these hypothetical design flows:

• \(Q_{10}=80\ \mathrm{m^3/s}\)

• \(Q_{50}=120\ \mathrm{m^3/s}\)

• \(Q_{100}=150\ \mathrm{m^3/s}\)

These numbers are examples only. They are not design estimates for any particular catchment.

Use the synthetic rating curve to identify the stage corresponding to each discharge:

Here, \(f^{-1}\) represents the inverse of the stage–discharge relationship. If the relationship is represented by a discrete table, use interpolation between the appropriate calculated stages.

If a cross-section’s rating curve does not extend to the target discharge, extend the hydraulic calculations using defensible geometry and roughness assumptions rather than blindly extrapolating the curve.

Step 5: Map flood water-surface elevations

A water-surface elevation is an absolute elevation referenced to a vertical datum. It is not the same as flood depth.

Suppose the synthetic rating curve provides a design stage at a particular river cross-section. That elevation can be used to estimate the water level near the cross-section, but it does not automatically describe the water surface across the entire river reach.

For a first-pass GIS model, water levels can be assigned to river stations and interpolated longitudinally. The resulting surface is then extended over the floodplain subject to terrain connectivity and hydraulic assumptions.

5.1 Interpolate water levels along the river

Create a point layer at the river cross-sections and add fields for:

• Q10 — 10-year design discharge.

• WSE10 — estimated 10-year water-surface elevation.

• WSE50 — estimated 50-year water-surface elevation.

• WSE100 — estimated 100-year water-surface elevation.

Repeat the same process for all cross-sections along the reach.

Use a linearly interpolated water level between adjacent stations only when that approximation is reasonable. More complex reaches may require longitudinal hydraulic calculations that account for energy losses, channel geometry, and backwater.

In QGIS, an initial continuous surface can be generated with an interpolation tool such as TIN interpolation or IDW interpolation, using the relevant water-surface elevation attribute.

Generate separate rasters for the three events.

Critical limitation: Ordinary IDW or TIN interpolation is not a hydraulic water-surface solver. It can create a visually continuous elevation surface that crosses hills, ridges, or levees incorrectly. Interpolation should be constrained by the river network and hydraulic structure of the reach; its results must be checked against cross-sections and known hydraulic controls.

A defensible simplified approach should distinguish between:

1. The water-surface profile along the river.

2. The floodplain water surface connected to the channel.

3. Areas hydraulically separated by levees, high ground, or other barriers.

A single flat water level across an entire floodplain is only a reasonable approximation for certain local applications, not a universal assumption.

Step 6: Calculate flood depth using the raster calculator

Once a water-surface elevation raster has been prepared for a design event, subtract the DEM ground elevation from the water-surface elevation.

The governing equation is:

where:

• \(D(x,y)\) is the calculated water depth at cell \((x,y)\).

• \(WSE(x,y)\) is the estimated water-surface elevation.

• \(DEM(x,y)\) is the ground elevation.

For mapping, negative depths and dry cells should not be displayed as positive inundation depths. Use a threshold and retain NoData values where the model has no valid water-surface estimate.

6.1 Calculate the 10-year flood depth

Open Raster → Raster Calculator in QGIS.

If the raster layers are named WSE_10yr and DEM, use the expression:

if(
  "WSE_10yr@1" > "DEM@1",
  "WSE_10yr@1" - "DEM@1",
  0
)

Save the output as FloodDepth_10yr.tif.

This expression sets cells with ground elevations above the water surface to zero. If NoData propagation or valid-data masks are important in your dataset, explicitly preserve the valid water-surface and terrain masks rather than treating every missing value as dry.

6.2 Calculate the 50-year flood depth

Use the corresponding 50-year water-surface raster:

if(
  "WSE_50yr@1" > "DEM@1",
  "WSE_50yr@1" - "DEM@1",
  0
)

Save as FloodDepth_50yr.tif.

6.3 Calculate the 100-year flood depth

Use:

if(
  "WSE_100yr@1" > "DEM@1",
  "WSE_100yr@1" - "DEM@1",
  0
)

Save as FloodDepth_100yr.tif.

All inputs must share a compatible elevation datum and units. If the DEM is in metres and the water-surface elevations are in a different datum or unit, the subtraction will be invalid until they are reconciled.

6.4 Convert flood depth into an inundation extent

Create a binary flood mask from the depth raster. For example, if you want to map cells with more than 0.10 m of modeled water depth:

if(
  "FloodDepth_100yr@1" > 0.10,
  1,
  0
)

Save the output as FloodExtent_100yr.tif.

Repeat the calculation for the 10-year and 50-year events.

The 0.10 m threshold is an illustrative cartographic cutoff, not a universal definition of flooding. Choose an appropriate threshold for the DEM accuracy, modeling purpose, and minimum depth of interest.

Do not assume that every positive-depth cell is physically inundated. A simple raster subtraction can identify isolated depressions and areas behind terrain barriers. Where connectivity matters, apply a suitable terrain-connectivity analysis and, ideally, a hydraulic method that accounts for the flow paths between the river and the floodplain.

Step 7: Validate flood extents and classify flood hazards

After calculating depth and extent, inspect the output for implausible patterns.

Check whether:

• The flood extends continuously from the river into connected low-lying terrain.

• High ground, levees, and embankments act as expected.

• Bridges and culverts are represented adequately.

• Inundation areas are plausible compared with observed flood records or authoritative flood maps.

• Deeper water occurs in locations consistent with the assumed terrain and water-surface profile.

• Larger design events produce reasonable changes in extent and depth.

For a simple preliminary hazard map, flood depth can be classified into illustrative categories:

These thresholds are for visualization, not universal safety or regulatory standards. Hazard also depends on velocity, duration, debris, rate of rise, and exposure.

To create a more useful flood-risk map, overlay the inundation results with buildings, roads, schools, health facilities, agricultural land, population data, and other assets. Keep hazard (flood depth, extent, velocity) distinct from risk (potential consequences for exposed people and assets).

3. Improving the workflow with hydraulic connectivity

A flood-depth raster can look convincing while still being hydraulically unrealistic. One of the most important quality checks is determining whether a low-lying pixel can actually be reached by floodwater.

For example, a depression behind a natural ridge might have an elevation below the modeled water level, yet remain dry because there is no hydraulic connection to the river.

A simplified GIS workflow can improve its screening results by:

1. Restricting the analysis to the relevant river corridor and floodplain.

2. Identifying terrain barriers and artificial embankments.

3. Evaluating whether inundated cells are connected to the river or another valid source of floodwater.

4. Investigating isolated flooded patches instead of automatically accepting them.

5. Comparing results against known flood extents, if available.

Terrain-connectivity filters can reduce obvious mapping artifacts, but they do not reproduce the movement of water through time or determine flow velocity. Where levees, culverts, bridges, and multiple flow paths control flooding, a hydraulic model is preferable.

4. Limitations: Simplified GIS modeling versus HEC-RAS

Synthetic rating curves and DEM-based inundation modeling offer a practical starting point when data and computing resources are limited. However, their assumptions must be understood before the results are used for planning or engineering.

The US Army Corps of Engineers’ HEC-RAS software supports one-dimensional steady and unsteady flow modeling and two-dimensional unsteady flow modeling. For authoritative technical guidance, consult the official HEC-RAS documentation.

HEC-RAS is not automatically accurate simply because it is more sophisticated. Poor terrain data, unsuitable roughness coefficients, incorrect boundary conditions, and insufficient calibration can also produce misleading results.

Sources of uncertainty to report

A credible flood-mapping report should document at least the following:

• DEM uncertainty: Vertical errors can be significant relative to shallow flood depths.

• Bathymetric uncertainty: Missing submerged channel geometry can distort discharge estimates.

• Roughness uncertainty: Manning’s \(n\) affects calculated conveyance and stage.

• Hydrological uncertainty: Estimated 10-, 50-, and 100-year discharges depend on the quality and length of the flow record and the selected frequency method.

• Hydraulic uncertainty: A uniform-flow approximation may be inappropriate in reaches affected by backwater, constrictions, or rapid changes in channel geometry.

• Spatial interpolation uncertainty: Interpolated water surfaces may cross barriers or misrepresent longitudinal gradients.

• Connectivity uncertainty: Raster subtraction alone cannot establish whether water can physically reach each cell.

For floodplain planning, sensitivity testing is particularly valuable. Recalculate the synthetic rating curve and inundation maps using plausible alternative roughness coefficients, channel slopes, and design discharges. Compare the changes in maximum depth and inundated area rather than reporting a single deterministic map as if it were exact.

5. Recommended outputs and deliverables

A well-documented QGIS project should contain the following layers and supporting data.

Use consistent map extents, legends, units, and color ramps across the three design events so that the differences in flood depth and extent can be compared directly.

Summary

Flood risk mapping with synthetic rating curves and DEMs combines simplified open-channel hydraulics with spatial terrain analysis. The essential workflow is to extract river cross-sections, calculate wetted area and hydraulic radius, apply Manning’s equation to construct stage–discharge relationships, estimate design water levels, and subtract terrain elevations from water-surface elevations to generate flood-depth maps.

The most important equations are:

These calculations support a practical first-pass analysis of potential inundation. Their reliability depends on the quality of the DEM, realistic channel geometry, defensible roughness and slope assumptions, appropriate design discharges, and a careful assessment of hydraulic connectivity.

Final recommendation: Use this approach for exploratory mapping and preliminary floodplain screening. For flood-risk decisions involving public safety, critical infrastructure, regulatory flood boundaries, or engineering design, validate the results against observed floods and use an appropriate calibrated hydraulic model, such as HEC-RAS, wherever the consequences justify it.